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  • ! Present Value and The Opportunity Cost of Capital

    Principles of Corporate FinanceBrealey and Myers Sixth Edition

    Slides by

    Matthew Will Chapter 2

    The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

    2- 2

    Topics Covered

    " Present Value" Net Present Value" NPV Rule" ROR Rule" Opportunity Cost of Capital" Managers and the Interests of Shareholders

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Present Value

    Present Value

    Value today of a future cash

    flow.

    Discount Rate

    Interest rate used to compute

    present values of future cash flows.

    Discount Factor

    Present value of a $1 future payment.

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Present Value

    1factordiscount =PV

    PV=ValuePresent

    C

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Present Value

    Discount Factor = DF = PV of $1

    Discount Factors can be used to compute the present value of any cash flow.

    DFr t

    =+1

    1( )

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Valuing an Office Building

    Step 1: Forecast cash flowsCost of building = C0 = 350Sale price in Year 1 = C1 = 400

    Step 2: Estimate opportunity cost of capitalIf equally risky investments in the capital marketoffer a return of 7%, then

    Cost of capital = r = 7%

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Valuing an Office Building

    Step 3: Discount future cash flows

    Step 4: Go ahead if PV of payoff exceeds investment

    374)07.1( 400)1( 1 === ++rCPV

    24374350 =+=NPV

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Net Present Value

    rC+

    +1

    C=NPV

    investment required-PV=NPV

    10

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Risk and Present Value

    " Higher risk projects require a higher rate of return.

    " Higher required rates of return cause lower PVs.

    374.071

    400PV

    7%at $400 C of PV 1

    =+

    =

    =

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Risk and Present Value

    374.071

    400PV

    7%at $400 C of PV 1

    =+

    =

    =

    357.121

    400PV

    12%at $400 C of PV 1

    =+

    =

    =

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Rate of Return Rule

    " Accept investments that offer rates of return in excess of their opportunity cost of capital

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Rate of Return Rule

    " Accept investments that offer rates of return in excess of their opportunity cost of capital.

    Example

    In the project listed below, the foregone investment opportunity is 12%. Should we do the project?

    14%or .14350,000

    350,000400,000investment

    profitReturn ===

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Net Present Value Rule

    " Accept investments that have positive net present value

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Net Present Value Rule

    " Accept investments that have positive net present value.

    ExampleSuppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return?

    55.4$1.1060+-50=NPV =

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Opportunity Cost of Capital

    ExampleYou may invest $100,000 today. Depending on the state of the economy, you may get one of three possible cash payoffs:

    140,000110,000$80,000PayoffBoomNormalSlumpEconomy

    000,110$3

    000,140000,100000,80C payoff Expected 1 =++==

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Opportunity Cost of Capital

    Example - continuedThe stock is trading for $95.65. Depending on the state of the economy, the value of the stock at the end of the year is one of three possibilities:

    140110$80eStock PricBoomNormalSlumpEconomy

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Opportunity Cost of Capital

    Example - continuedThe stocks expected payoff leads to an expected return.

    15%or 15.65.95

    65.95110profit expectedreturn Expected

    110$3

    14010080C payoff Expected 1

    ===

    =++==

    investment

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Opportunity Cost of Capital

    Example - continuedDiscounting the expected payoff at the expected return leads to the PV of the project.

    650,95$1.15

    110,000PV ==

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Investment vs. Consumption

    " Some people prefer to consume now. Some prefer to invest now and consume later. Borrowing and lending allows us to reconcile these opposing desires which may exist within the firms shareholders.

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Investment vs. Consumption

    A

    B

    100

    80

    60

    40

    20

    20202020 40 60 80 100income in period 0

    income in period 1

    Some investors will prefer Aand others B

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Investment vs. Consumption

    The grasshopper (G) wants to consume now. The ant (A) wants to wait. But each is happy to invest. A prefers to invest 14%, moving up the red arrow, rather than at the 7% interest rate. G invests and then borrows at 7%, thereby transforming $100 into $106.54 of immediate consumption. Because of the investment, G has $114 next year to pay off the loan. The investments NPV is $106.54-100 = +6.54

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Investment vs. Consumption" The grasshopper (G) wants to consume now.

    The ant (A) wants to wait. But each is happy to invest. A prefers to invest 14%, moving up the red arrow, rather than at the 7% interest rate. G invests and then borrows at 7%, thereby transforming $100 into $106.54 of immediate consumption. Because of the investment, G has $114 next year to pay off the loan. The investments NPV is $106.54-100 = +6.54

    100 106.54 Dollars Now

    Dollars Later

    114

    107

    A invests $100 now and consumes $114 next year

    G invests $100 now, borrows $106.54 and consumes now.

  • The McGraw-Hill Companies, Inc., 2000Irwin/McGraw Hill

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    Managers and Shareholder Interests

    " Tools to Ensure Management Responsiveness

    # Subject managers to oversight and review by specialists.

    # Internal competition for top level jobs that are appointed by the board of directors.

    # Financial incentives such as stock options.